Redington Pass has it all, from graded FS roads to moderate Jeep trails to AA expert single track. Here's a map.
For low desert dirt riding, South Wilmot road is a great jumping off point. Head South from Wilmot & Valencia.
South of town the Santa Ritas have miles and miles of riding too. Map.
If you're interested in some paved twisties, the Catalina Highway is breathtaking, and the roads that run through Saguaro Park West are scenic and curvy with lots of good places to stop for photo ops.
I work M-F, but if you'd like a tour guide for some mild-moderate stuff I can see about getting a day off. PM me if you're interested and we'll set it up.